Huaizhen Chen, Junxiao Li, and Kristopher A. Innanen

ABSTRACT

Based on a model of attenuative cracked rock, we derive a simplified and frequencydependent
stiffness matrix in the case that the rock contains aligned partially saturated
cracks, and in the stiffness matrix we also involve the effect of pressure relaxation that
is a sensitive fluid factor directly influenced by fluid viscosity and saturation. Using perturbation
in stiffness matrix for an interface separating two attenuative cracked media and
relationship between scattering potential and reflection coefficient, we propose a linearized
reflection coefficient in the case of P-wave incidence and P-wave scattering, which is a
azimuth- and frequency-dependent function of dry rock elastic property, dry fracture weaknesses
and pressure relaxation related parameter. Using difference in the reflection coefficients
between azimuthal angles, we derive an expression of Quasi-difference in Elastic
Impedance (QδEI) that is mainly affected by dry fracture weaknesses and pressure relaxation
related parameter. Using the derived QδEI, we establish an inversion approach of
employing frequency-dependent differences in seismic amplitudes to estimate dry fracture
weaknesses and pressure relaxation related parameter. Applying the established approach
to synthetic datasets, we conclude the approach can obtain acceptable inversion results of
dry fracture weaknesses and pressure relaxation related parameter in the case of generated
synthetic data containing a moderate signal-to-noise ratio (SNR). Test on a real data set reveals
that the inversion results of dry fracture weaknesses provide a reliable tool in fracture
prediction, and the estimated pressure relaxation related parameter appear as an additional
proof for the discrimination of fluids in cracks.